1. The problem statement, all variables and given/known data Prove that lim (1/x) x --> 0 does not exist, i.e., show that lim (1/x) x --> 0 = l is false for every number l. 2. Relevant equations 0 < |x-a| < d |f(x) - l| < E 3. The attempt at a solution The strange thing is, the first time through I got the same solution as Spivak, but looking over it again the logic seems downright wrong. Here's the solution, verbatim: Where is he getting the bold portion from? I write |1/x - l| < E |1/x| - |l| < |1/x - l| < E |1/x| - |l| < E |1/x| < E + |l| How is he getting greater-than?